Real values of the W-function

Approximations for real values of W(x), where W is defined by solutions of W exp(W) = x, are presented. All of the approximations have maximum absolute (|W|>1) or relative (|W|<1) errors of O(10−4). With these approximations an efficient algorithm, consisting of a single iteration of a rapidly converging iteration scheme, gives estimates of W (x) accurate to at least 16 significant digits (15 digits if double precision is used). The Fortran code resulting from the algorithm is written to account for the different floating-point- number mantissa lengths on different computers, so that W (x) is computed to the floating-point precision available on the host machine.